To infer this new statement, the islanders have to be aware that the others are listening, they understand, they know that everyone understands, etc. etc. That

To infer this new statement, the islanders have to be aware that the others are listening, they understand, they know that everyone understands, etc. etc. That's deeply unsatisfying because we are told that everyone is capable of making the observation that is communicated right from the beginning for n > 1. What prevents the group from acting as soon as the situation starts but before the foreigner speaks? The message adds information to the system but it is not that there is one person with blue eyes, i.e. what was explicitly stated. I think it adds information about the time at which an action will or will not occur. The information passed is "you can expect something to happen to the people with blue eyes tomorrow."